A standard abstract interpretation expresses numeric properties using
a numeric abstract domain, of which the most common are
intervals (also known as boxes) and convex polyhedra.
Intervals [1]} define abstract states using
inequalities of the form \(p~\mathit {relop}~n\)  where \(p\)  is a
variable, \(n\)  is a constant integer, and \(\mathit {relop}\)  is a relational
operator such as \(\le \) . A variable such as \(p\)  is sometimes called a
dimension, as it describes one axis of a numeric space.
Convex polyhedra [2]} define abstract
states using linear relationships between variables and constants,
e.g., of the form \(3p_1 - p_2 \le 5\) .
Intervals are less precise but more efficient than polyhedra.
Operation on intervals have time complexity linear in the number of
dimensions whereas the time complexity for polyhedra operations is
exponential in the number of dimensions.Further, the time
complexity of join is \(O(d \cdot c^{2^{d+1}})\)  where \( c \)  is the
number of constraints, and \( d \)  is the number of
dimensions [3]}.
